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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 20th 2019

stub entry, for the moment just so as to record references

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeAug 20th 2019

added statement of the basic Tietze-Gleason extension theorem (here), as in Palais 60, Theorem 1.4.3

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMar 21st 2021
• (edited Mar 21st 2021)

added statement of other/more general conditions for the equivariant extension to exist (from Jaworowski 76, Lashof 81):

1. the ambient domain G-space $X$ is

1. locally comact

2. separable

3. metrizable

4. finite-dimensional (?)

5. with a finite number of orbit types.

2. the codomain G-space is such that

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMar 21st 2021

have further expanded out the statement of the “Jaworowski extension theorem” (here), following Lashof.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMar 21st 2021
• (edited Mar 21st 2021)

fixed the condition on $A\subset X$: it needs to be a (closed) sub-$G$-space of $X$, not necessarily a subspace of $X^G$

(Palais60 and Lashof81 and many other authors say “invariant subspace”, which is ambiguous – but checking in Jaworowski clarifies it)

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